Special Functions And Generalized Sturm Liouville Problems

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Special Functions And Generalized Sturm Liouville Problems

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Author : Mohammad Masjed-Jamei
language : en
Publisher: Springer Nature
Release Date : 2020-01-25

Special Functions And Generalized Sturm Liouville Problems written by Mohammad Masjed-Jamei and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2020-01-25 with Mathematics categories.

This book discusses theoretical and applied aspects of Sturm-Liouville theory and its generalization. It introduces and classifies generalized Sturm-Liouville problems in three different spaces: continuous, discrete, and q-discrete spaces, focusing on special functions that are solutions of a regular or singular Sturm-Liouville problem. Further, it describes the conditions under which the usual Sturm-Liouville problems with symmetric solutions can be extended to a larger class, particularly highlighting the solutions of generalized problems that result in new orthogonal sequences of continuous or discrete functions. Sturm-Liouville theory is central to problems in many areas, such as engineering, mathematics, physics, and biology. This accessibly written book on the topic is a valuable resource for a broad interdisciplinary readership, from novices to experts.

Sturm Liouville Theory

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Author : Werner O. Amrein
language : en
Publisher: Springer Science & Business Media
Release Date : 2005-05-19

Sturm Liouville Theory written by Werner O. Amrein and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2005-05-19 with Mathematics categories.

This is a collection of survey articles based on lectures presented at a colloquium and workshop in Geneva in 2003 to commemorate the 200th anniversary of the birth of Charles François Sturm. It aims at giving an overview of the development of Sturm-Liouville theory from its historical roots to present day research. It is the first time that such a comprehensive survey has been made available in compact form. The contributions come from internationally renowned experts and cover a wide range of developments of the theory. The book can therefore serve both as an introduction to Sturm-Liouville theory and as background for ongoing research. The volume is addressed to researchers in related areas, to advanced students and to those interested in the historical development of mathematics. The book will also be of interest to those involved in applications of the theory to diverse areas such as engineering, fluid dynamics and computational spectral analysis.

An Introduction To Partial Differential Equations With Matlab

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Author : Matthew P. Coleman
language : en
Publisher: CRC Press
Release Date : 2016-04-19

An Introduction To Partial Differential Equations With Matlab written by Matthew P. Coleman and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2016-04-19 with Mathematics categories.

An Introduction to Partial Differential Equations with MATLAB, Second Edition illustrates the usefulness of PDEs through numerous applications and helps students appreciate the beauty of the underlying mathematics. Updated throughout, this second edition of a bestseller shows students how PDEs can model diverse problems, including the flow of heat,

Mathematical Methods For Scientists And Engineers

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Author : Donald Allan McQuarrie
language : en
Publisher: University Science Books
Release Date : 2003

Mathematical Methods For Scientists And Engineers written by Donald Allan McQuarrie and has been published by University Science Books this book supported file pdf, txt, epub, kindle and other format this book has been release on 2003 with Mathematics categories.

"Intended for upper-level undergraduate and graduate courses in chemistry, physics, math and engineering, this book will also become a must-have for the personal library of all advanced students in the physical sciences. Comprised of more than 2000 problems and 700 worked examples that detail every single step, this text is exceptionally well adapted for self study as well as for course use."--From publisher description.

Mathematical Methods For Engineers And Scientists 3

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Author : Kwong-Tin Tang
language : en
Publisher: Springer Science & Business Media
Release Date : 2006-11-30

Mathematical Methods For Engineers And Scientists 3 written by Kwong-Tin Tang and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2006-11-30 with Science categories.

Pedagogical insights gained through 30 years of teaching applied mathematics led the author to write this set of student oriented books. Topics such as complex analysis, matrix theory, vector and tensor analysis, Fourier analysis, integral transforms, ordinary and partial differential equations are presented in a discursive style that is readable and easy to follow. Numerous examples, completely worked out, together with carefully selected problem sets with answers are used to enhance students' understanding and manipulative skill. The goal is to make students comfortable in using advanced mathematical tools in junior, senior, and beginning graduate courses.

Q Fractional Calculus And Equations

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Author : Mahmoud H. Annaby
language : en
Publisher: Springer
Release Date : 2012-08-27

Q Fractional Calculus And Equations written by Mahmoud H. Annaby and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-08-27 with Mathematics categories.

This nine-chapter monograph introduces a rigorous investigation of q-difference operators in standard and fractional settings. It starts with elementary calculus of q-differences and integration of Jackson’s type before turning to q-difference equations. The existence and uniqueness theorems are derived using successive approximations, leading to systems of equations with retarded arguments. Regular q-Sturm–Liouville theory is also introduced; Green’s function is constructed and the eigenfunction expansion theorem is given. The monograph also discusses some integral equations of Volterra and Abel type, as introductory material for the study of fractional q-calculi. Hence fractional q-calculi of the types Riemann–Liouville; Grünwald–Letnikov; Caputo; Erdélyi–Kober and Weyl are defined analytically. Fractional q-Leibniz rules with applications in q-series are also obtained with rigorous proofs of the formal results of Al-Salam-Verma, which remained unproved for decades. In working towards the investigation of q-fractional difference equations; families of q-Mittag-Leffler functions are defined and their properties are investigated, especially the q-Mellin–Barnes integral and Hankel contour integral representation of the q-Mittag-Leffler functions under consideration, the distribution, asymptotic and reality of their zeros, establishing q-counterparts of Wiman’s results. Fractional q-difference equations are studied; existence and uniqueness theorems are given and classes of Cauchy-type problems are completely solved in terms of families of q-Mittag-Leffler functions. Among many q-analogs of classical results and concepts, q-Laplace, q-Mellin and q2-Fourier transforms are studied and their applications are investigated.

A Short Course In Mathematical Methods With Maple

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Author : Henrik Aratyn
language : en
Publisher: World Scientific
Release Date : 2006

A Short Course In Mathematical Methods With Maple written by Henrik Aratyn and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2006 with Mathematics categories.

This unique book provides a streamlined, self-contained and modern text for a one-semester mathematical methods course with an emphasis on concepts important from the application point of view. Part I of this book follows the ?paper and pencil? presentation of mathematical methods that emphasizes fundamental understanding and geometrical intuition. In addition to a complete list of standard subjects, it introduces important, contemporary topics like nonlinear differential equations, chaos and solitons. Part II employs the Maple software to cover the same topics as in Part I in a computer oriented approach to instruction. Using Maple liberates students from laborious tasks while helping them to concentrate entirely on concepts and on better visualizing the mathematical content. The focus of the text is on key ideas and basic technical and geometric insights presented in a way that closely reflects how physicists and engineers actually think about mathematics.

Special Functions And Analysis Of Differential Equations

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Author : Praveen Agarwal
language : en
Publisher: CRC Press
Release Date : 2020-09-08

Special Functions And Analysis Of Differential Equations written by Praveen Agarwal and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2020-09-08 with Mathematics categories.

Differential Equations are very important tools in Mathematical Analysis. They are widely found in mathematics itself and in its applications to statistics, computing, electrical circuit analysis, dynamical systems, economics, biology, and so on. Recently there has been an increasing interest in and widely-extended use of differential equations and systems of fractional order (that is, of arbitrary order) as better models of phenomena in various physics, engineering, automatization, biology and biomedicine, chemistry, earth science, economics, nature, and so on. Now, new unified presentation and extensive development of special functions associated with fractional calculus are necessary tools, being related to the theory of differentiation and integration of arbitrary order (i.e., fractional calculus) and to the fractional order (or multi-order) differential and integral equations. This book provides learners with the opportunity to develop an understanding of advancements of special functions and the skills needed to apply advanced mathematical techniques to solve complex differential equations and Partial Differential Equations (PDEs). Subject matters should be strongly related to special functions involving mathematical analysis and its numerous applications. The main objective of this book is to highlight the importance of fundamental results and techniques of the theory of complex analysis for differential equations and PDEs and emphasizes articles devoted to the mathematical treatment of questions arising in physics, chemistry, biology, and engineering, particularly those that stress analytical aspects and novel problems and their solutions. Specific topics include but are not limited to Partial differential equations Least squares on first-order system Sequence and series in functional analysis Special functions related to fractional (non-integer) order control systems and equations Various special functions related to generalized fractional calculus Operational method in fractional calculus Functional analysis and operator theory Mathematical physics Applications of numerical analysis and applied mathematics Computational mathematics Mathematical modeling This book provides the recent developments in special functions and differential equations and publishes high-quality, peer-reviewed book chapters in the area of nonlinear analysis, ordinary differential equations, partial differential equations, and related applications.

Sampling Theory In Fourier And Signal Analysis Advanced Topics

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Author : J. R. Higgins
language : en
Publisher: Oxford University Press
Release Date : 1999-11-25

Sampling Theory In Fourier And Signal Analysis Advanced Topics written by J. R. Higgins and has been published by Oxford University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 1999-11-25 with Mathematics categories.

Volume 1 in this series laid the mathematical foundations of sampling theory; Volume 2 surveys the many applications of the theory both within mathematics and in other areas of science. Topics range over a wide variety of areas, and each application is given a modern treatment.

Advances In Shannon S Sampling Theory

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Author : AhmedI. Zayed
language : en
Publisher: Routledge
Release Date : 2018-04-24

Advances In Shannon S Sampling Theory written by AhmedI. Zayed and has been published by Routledge this book supported file pdf, txt, epub, kindle and other format this book has been release on 2018-04-24 with Mathematics categories.

Advances in Shannon's Sampling Theory provides an up-to-date discussion of sampling theory, emphasizing the interaction between sampling theory and other branches of mathematical analysis, including the theory of boundary-value problems, frames, wavelets, multiresolution analysis, special functions, and functional analysis. The author not only traces the history and development of the theory, but also presents original research and results that have never before appeared in book form. Recent techniques covered include the Feichtinger-Gröchenig sampling theory; frames, wavelets, multiresolution analysis and sampling; boundary-value problems and sampling theorems; and special functions and sampling theorems. The book will interest graduate students and professionals in electrical engineering, communications, and applied mathematics.